document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197439>Question 1197439</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There is a gambling game where equal-weight balls with numbers ranging from 1 to 15 are placed inside a tambiolo and mixed. Without replacement, three balls are chosen at random and are then chosen one by one.\r<BR>\n" );
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document.write( "(a) A certain casino customer named Mr. Han only has enough cash to place a total of 5 bets that evening. Mr. Han consistently bets that the 3 balls will be chosen, and that the greatest number will be at least as large as \"12\" among them. How likely is it that this will  happen?\r<BR>\n" );
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document.write( "(b) What is the likelihood that Mr. Han will finally strike it lucky and win on the 5th bet after a run of bad luck? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830959 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20054)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=830959\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Mr. Han will lose if the 3 balls are all chosen from balls 1 through 11.<BR>\n" );
document.write( "That's 11C3 = 165 ways.\r<BR>\n" );
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document.write( "There are 15C3 = 455 ways the 3 balls can be selected, so there are 455-165=290<BR>\n" );
document.write( "ways he can win.\r<BR>\n" );
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document.write( "So the probability that he wins a bet is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=290%2F455 ALIGN=MIDDLE  ALT=\"290%2F455\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=58%2F91 ALIGN=MIDDLE  ALT=\"58%2F91\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "That's the answer to (a)\r<BR>\n" );
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document.write( "The probability that he loses a bet is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-+58%2F91+=+33%2F91 ALIGN=MIDDLE  ALT=\"1+-+58%2F91+=+33%2F91\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  So the probability that he loses the first 4 and wins on the 5th is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2833%2F91%29%5E4%2858%2F91%29 ALIGN=MIDDLE  ALT=\"%2833%2F91%29%5E4%2858%2F91%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is about 0.011\r<BR>\n" );
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document.write( "Edwin</pre>\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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